Technical Report
Vivienne Maxwell and Kiehl Jones
5/4/2019
I. Abstract
Many political scientists have theorized that democratic institutions reduce the overall rates of violence in the world, as democratic institutions facilitate cooperation within and among nations. Our aim is to analyze various levels of violence within nations to determine whether democratic institutions — typically in the form of democratic governments — reduce overall rates of violence. Essentially, our main question is whether the increase in democratic institutions results in a more peaceful world.
II. Introduction
A body of political science literature covering the impacts of democratic nations and levels of world-wide violence has been published in recent years. The 20th century has been full of political turmoil. The demise of British hegemony and ensuing de-colonization culminated in two world wars, which disrupted society. The cold war period resulted in an increased fear of communism. As nations began to form, there was fear from the West that these countries would adopt non-democratic governments. On a similar note, political scientists have commented on the rise of democratic nations and the decreased levels of world-wide violence. Some have even attributed causality between the two. The goal of this project was to test whether democratic nations do result in a more peaceful world. The implications of this are significant. If democratic nations really are more peaceful, then there are benefits to newly formed nations to adopt this type of government. Testing the validity of this theory is also important: is this theory legitimate or is this just Western democratic nations trying to push democracy onto forming governments in the hopes of preventing the spread of communism? This project aims to tackle these questions by testing whether democratic nations are less violent than non-democratic nations.
III. Data
In order to test this political theory, we first randomly selected 50 countries in order to make statistical inference about the existing 195 countries. We separated the 50 countries into democratic and non-democratic nations. Democracy was established using the Varieties of Democracy dataset (V-Dem) illustrated in the tables below. We used three indicators to determine democracy: (1) Freedom of discussion, (2) Access to Justice, (3) Clean Elections, which was based on a clean election index. Each of the indicators were given a likelihood index between 0 and 1, where 0 meant that the indicator was unlikely to be present and 1 meant that the indicator was very likely to be present. We defined nations as democratic if their index was greater than or equal to 0.75.
The index was determined by five expert social science research methodologists. However, the indices are somewhat subjective as they were determined by research methodologists. One could argue that there is always some level of bias present when a decision is made by a human. This could result in potential biases for our definition of a democracy. We also used a high index requirement of 0.75. If we accepted nations with indexes greater than or equal to 0.5, our data may have been different as nations previously coded as non-democratic would now be considered democratic. Therefore, there are some potential biases in our coding of democratic and non-democratic nations.
| Entity | Democracy |
|---|---|
| Italy | Y |
| Czech Republic | Y |
| Greece | Y |
| Finland | Y |
| Germany | Y |
| Sweden | Y |
| Panama | Y |
| Poland | Y |
| Slovakia | Y |
| Benin | Y |
| Austria | Y |
| Uruguay | Y |
| Tunisia | Y |
| Australia | Y |
| United Kingdom | Y |
| United States America | Y |
| Entity | Democracy |
|---|---|
| Malaysia | N |
| Ethiopia | N |
| Congo | N |
| Mali | N |
| Yemen | N |
| Jordan | N |
| Bhutan | N |
| Rwanda | N |
| Kyrgyzstan | N |
| Nicaragua | N |
| China | N |
| Uzbekistan | N |
| Togo | N |
| Croatia | N |
| Sierra Leone | N |
| Timor | N |
| Liberia | N |
| Albania | N |
| Senegal | N |
| Burkina Faso | N |
| Cambodia | N |
| Dominican Republic | N |
| Bolivia | N |
| Moldova | N |
| Serbia | N |
| Iran | N |
This map color-codes all of the 50 countries used in the data anaylses and visualizations. Green represents democratic nations, Red is non-democratic nations, and yellow are unknown governments according to V-Dem Varieties of Democracy.
To determine levels of violence we used the following four data sets: Homicide rates for 2016 (United Nations), Prison Populations for 2016 (United Nations), Battle Deaths due to civil conflict from 1946 to 2008 (PRIO) and the frequency of Extrajudicial Killings in 2011 (CIRI). We acquired these data sets by doing a google search for international levels of violence.
Homicide Rates
Homicide rates were chosen as they are a universal indicator of violence within a nation. The data was collected from the United Nations, which we felt was a reliable source. The homicide rates were defined as homicides per 100,000 people and ranged from 0.6388674 (United Kingdom) to 21.0199629 (Bahamas). The cases for the data visualization were the 50 randomly selected countries, though we had missing data for the Bahamas, Greenland, Barbados, Micronesia, and the United States. For the statistical analyses, we calculated a difference in means between democratic and non-democratic nations, so the cases were 16 democratic nations (there was missing data for the United States) and 26 non-democratic nations. The variables used to conduct statistical analyses and create visualizations were Entity, Year, Rate, and Democracy. We filtered the data for the year 2016, as it was the year with the least unknown values from our sample countries, and in the visualizations, we color-coded the nations by their types of government (democratic, non-democratic, NA). The goal was to assess whether homicide rates were lower in democratic nations, as this could indicate that democracies have lower levels of violence.
Prison Population Rates
Our reasoning for using prison populations was that higher prison population rates would mean less violence in that nation. Data was collected from the United Nations, which we deemed a credible source. The prison populations rates were defined as prison population per 100,000 people and ranged from 98 (Austria) to 106 (Cambodia). The cases for the data visualizations were the 50 randomly selected nations, and the cases for the statistical analyses were 15 of the 16 democratic nations (data were missing for the US) and 22 of the 26 non-democratic nations (data were missing for Bolivia, Burkina Faso, Iran, and Moldova). The variables used were Entity, Year, Rate, and Democracy. We filtered the data for the year 2016, as it was the year with the least unknown values from our sample countries. In the visualizations, the type of government was color-coded (democratic, non-democratic, NA). The goal was to test whether prison population rates were lower in democratic nations.
Battle Deaths Due to Civil Conflict
According to some political scientists, civil conflict occurs more often in non-democratic nations. If this theory is true, we expected to see higher levels of battle deaths due to civil conflict in non-democratic nations. The data set was collected from The Peace Research Institute Oslo, which is “an independent research institution known for its effective synergy of basic and policy-relevant research” (PRIO). Battle deaths due to civil conflict were defined as “the use of armed force between two parties, of which at least one is the government of a state, results in at least 25 battle-related deaths” (PRIO). The cases used for the visualizations and analyses were the 50 randomly selected democratic and non-democratic nations. However, there were gaps in the data which meant we could not filter for one specific year. Therefore, we only filtered for the type of democracy. This meant that for the democratic nations, we had 33 cases and for non-democratic nations, we had 281 cases. Also, there were negative values for battle deaths which meant that no battle deaths were recorded. The variables used were Entity, Year, Death, and Democracy, where death was the number of battle deaths due to civil conflict. The main goal was to test the political theory that non-democratic nations have higher levels of civil conflict, which would be represented by higher levels of battle deaths due to civil conflict.
Civil Rights Violation
We sought to include various types of violence in our project. Extrajudicial killings, defined as “killings by government officials without due process of law” (CIRI), were selected because we felt we needed one indicator of violence in which the government infringed upon civilian rights. This data was collected from the CIRI Human Rights Project, which “contains standards-based quantitative information on government respect for 15 internationally recognized human rights for 202 countries, annually from 1981-2011” (CIRI). The cases for the data visualization and statistical analyses were 14 of the 16 democratic nations (data were missing for Slovakia and the US) and 23 of the 26 non-democratic nations (data were missing for Congo, Kyrgyzstan, and Timor). The variables used for this data set included Entity, Year, Kill, and Democracy, where Entity is the name of the country, and kill is the extrajudicial killing index. The death index ranges from 0 to 2, where 0 means the killings occur frequently and 2 means the killings hardly ever occur or they are not reported. The data was filtered for the year 2011. The goal was to assess whether non-democratic nations had higher frequencies of extra-judicial killings, as that could support our hypothesis that democratic nations have lower levels of violence.
IV. Methods
RStudio is an integrated development environment (IDE) for the programing language R and is used for statistical computing, analysis, and graphics. Using information from the V-Dem dataset, we created a CSV file called World_govt denoting our random sample of 50 countries as democratic or non-democratic. We coded a nation as democratic or non-democratic based on our three indicators, freedom of discussion, access to justice, and clean elections, where our cutoff value was greater than or equal to 0.75. We loaded all datasets, homicide_rate (United Nations), Prison_population (United Nations), Battle_Death (PRIO), and civil_rights (CIRI) into RStudio and wrangled the data for each level of violence category. The CSV file was loaded into RStudio and used to extract the 50 sample countries from each of the global datasets. It is crucial to note that if the name of a country in the CSV file did not match the name of the country in a level of violence dataset exactly, it would not be taken in as part of the analysis within RStudio. For each variable of measurement we conducted a hypothesis test using the difference of means with the following hypotheses for each category, where \(\mu_{HDem}\) is the mean level of violence for a democratic nation and \(\mu_{HNon}\) is the mean level of violence for a non-democratic nation:
\[H_{0} : \mu_{HDem} - \mu_{HNon} = 0 \]
\[H_{a} : \mu_{HDem} - \mu_{HNon} < 0 \]
Before analyzing our data we decided to use an alpha level of 5% to determine statistical significance. Any country that had unknown values in their respective category was not included in the calculations for the variable when measuring difference of means.
Homicide Rates
For the homicide rates dataset, the variables used for statistical analyses and visualizations were entity, year, rate, and democracy. We filtered the data for the year 2016 and used the filtered data to create a barplot. In the barplot we color-coded the nations by their types of government. Countries were organized top to bottom from highest homicide rates to lowest. Using the filtered dataset, we created a comparative summary statistic detailing the minimum value, first quartile, median, third quartile, maximum value, mean, standard deviation, and filtered counties present (n) for democratic and non-democratic nations separately. With the summary statistics we were able to calculated the t-statistic of our data using the equation for hypothesis test, \(t = (statistic - H_{0}) / SE\), in which the standard error (SE) for a difference in mean is equal to \(\sqrt{s_{1}^2 / n_{1} + s_{2}^2 / n_{2}}\). In RStudio we simulated a t-distribution, with degrees of freedom equal to the smaller of \(n_{1}-1\) and \(n_{2}-1\) to find the p-value given our t-statistic. We created a boxplot to analyze the difference in means of homicide rates in nations based on government type.
Prison Population
The prison population dataset used variables, entity, year, rate, and democracy for statistical analyses and visualizations. We filtered the data for the year 2016 and used the filtered data to create a barplot. In the barplot we color-coded the nations by their types of government. Using the filtered dataset, we created a comparative summary statistic detailing the minimum value, first quartile, median, third quartile, maximum value, mean, standard deviation, and filtered counties present (n) for democratic and non-democratic nations separately. With the summary statistics we were able to calculated the t-statistic of our data using the equation for hypothesis test, \(t = (statistic - H_{0}) / SE\), in which the standard error (SE) for a difference in mean is equal to \(\sqrt{s_{1}^2 / n_{1} + s_{2}^2 / n_{2}}\). In RStudio we simulated a t-distribution, with degrees of freedom equal to the smaller of \(n_{1}-1\) and \(n_{2}-1\) to find the p-value given our t-statistic.
Battle Deaths Due to Civil Conflict
Battle deaths due to civil conflict was distinguished by it variables, entity, year, death, and democracy. We filtered the data for by type of government—democracy or non-democracy—to make two separate barplots. The barplots were organized by filtered countries present from greatest to least battle deaths. We color-coded the barplots to further differentiate between the two types of governments. Using the filtered dataset, we created a comparative summary statistic detailing the minimum value, first quartile, median, third quartile, maximum value, mean, standard deviation, and filtered counties present (n) for democratic and non-democratic nations separately. With the summary statistics we were able to calculated the t-statistic of our data using the equation for hypothesis test, \(t = (statistic - H_{0}) / SE\), in which the standard error (SE) for a difference in mean is equal to\(\sqrt{s_{1}^2 / n_{1} + s_{2}^2 / n_{2}}\). In RStudio we simulated a t-distribution, with degrees of freedom equal to the smaller of \(n_{1}-1\) and \(n_{2}-1\) to find the p-value given our t-statistic.
Civil Rights Violation
Extrajudicial killings for the civil rights violations dataset was filtered for the year 2011 and by type of government—democracy or non-democracy—to make two separate dotplots. The variables used were entity, year, KILL, and democracy. Both dotplots organized the filtered countries present from highest frequency index (0) to lowest frequency index (2). We color-coded the doptplot to further differentiate between the two types of global institutions. Using the filtered dataset, we created a comparative summary statistic detailing the minimum value, first quartile, median, third quartile, maximum value, mean, standard deviation, and filtered the counties present (n) for democratic and non-democratic nations separately. With the summary statistics we were able to calculated the t-statistic of our data using the equation for hypothesis test, \(t = (statistic - H_{0}) / SE\), in which the standard error (SE) for a difference in mean is equal to \(\sqrt{s_{1}^2 / n_{1} + s_{2}^2 / n_{2}}\). In RStudio we simulated a t-distribution, with degrees of freedom equal to the smaller of \(n_{1}-1\) and \(n_{2}-1\) to find the p-value given our t-statistic.
V. Results
Homicide Rates
The barplot depicts the Bahamas, whose type of government is unknown, as having the highest homicide rate and the United Kingdom, a democratic country, as having the lowest homicide rate (Fig. 1a). Among democratic nations, the highest homicides rates were located in Panama—a total of 1,574,518 people per year—while the lowest homicide rates were found in the United Kingdom—total of 63,886.74 people per year. For non-democratic nations the highest homicide rates were located in the Dominican Republic, with an estimate of 1,348,376 people per year, while the lowest homicide rates were present in Burkina Faso, with an estimate of 91,656.11 people per year.
SUMMARY STATISTICS We identified 15 democratic nations and 26 non-democratic nations from our sample countries within the homicide rate dataset for our analysis. For democratic nations our first and third quartile for homicide rates per year were 0.909254 and 2.271686 respectively. The median homicide rates per year in democratic nations were 1.268179. On average democratic nations experience 2.579143 homicides in 2016, with a standard deviation of 3.828090. On the other hand, non-democratic nations had a first quartile of 2.052631 and a third quartile of 4.375431. The median homicide rates per year in non-democratic nations was 3.104113. Our data showed on average non-democratic institutions experience 3.969053 homicides per year with a standard deviation of 3.057837.
#Summary Statistics for Homicide Rates
sum_hom <- favstats( Rate ~ Democracy, data = foo)| Democracy | min | Q1 | median | Q3 | max | mean | sd | n | missing |
|---|---|---|---|---|---|---|---|---|---|
| N | 0.9165611 | 2.052631 | 3.104113 | 4.375431 | 13.48376 | 3.969053 | 3.057837 | 26 | 0 |
| Y | 0.6388674 | 0.909254 | 1.268179 | 2.271686 | 15.74518 | 2.579143 | 3.828091 | 15 | 0 |
DIFFERENCE IN MEANS In order to conduct a difference in means test, the amount of cases (n) must be greater than or equal to 30, or the data must be symmetric. Our conditions are not met for a difference in means because we have 16 democratic nations and 26 non-democratic nations and the data is right-skewed. However, for the sake of this report, we will continue on assuming that the conditions are met.
t.test(Rate ~ Democracy , data = foo)##
## Welch Two Sample t-test
##
## data: Rate by Democracy
## t = 1.2022, df = 24.356, p-value = 0.2408
## alternative hypothesis: true difference in means is not equal to 0
## 95 percent confidence interval:
## -0.9943315 3.7741507
## sample estimates:
## mean in group N mean in group Y
## 3.969053 2.579143The difference in mean homicide rates for non-democratic and democratic nations is not statistically significant. With a p-value of 0.2408, we fail to reject the null hypothesis that the mean rates of homicide in democratic and non-democratic nations are equal. This test is inconclusive.
Descriptive Analysis: Mean Homicide Rates Between Democractic and Non-Democratic Nations
This boxplot depicts the difference in means of homicide rates between democratic and non-democratic governments. As illustrated, non-democratic nations have a higher mean of homicide rates (3.969053) compared to democratic nations (2.579143). However, it is essential to note that although homicide rates appear higher in non-democratic nations, this difference in means is not statistically significant.
95% CONFIDENCE INTERVAL In order to conduct a confidence interval the data must be bell-shaped and symmetrical.
The data are not bell-shaped or symmetrical—they are right skewed—so the conditions to run a 95% confidence interval are not met. However, for the sake of this report, we will continue on assuming that the conditions are met.
## Single numerical variable
## n = 26, y-bar = 3.9691, s = 3.0578
## 95% CI: (2.734 , 5.2041)
The 95% confidence interval for the mean rates of homicide rates in non-democratic nations is (2.734 , 5.2041). Therefore, we are 95% confident that the mean homicide rates in non-democratic nations is between 2.734 and 5.2041 per 100,000 people.
Prison Population
In figure 2, there appears to be a trend between a nation’s prison rates and whether that nation is democratic or non-democratic. However, the relationship between these two variables is not statistically significant. With a p-value of 0.3483, we find no evidence of a correlation between prison population rates and the type of government. Overall, the United States has the highest prison population rates (718 per 100,000 people), and Burkina Faso has the lowest prison population rates (28 per 100,000 people).
t.test(Rate.y ~ Democracy , data = prison_population)##
## Welch Two Sample t-test
##
## data: Rate.y by Democracy
## t = -0.95231, df = 31.099, p-value = 0.3483
## alternative hypothesis: true difference in means is not equal to 0
## 95 percent confidence interval:
## -96.68764 35.13007
## sample estimates:
## mean in group N mean in group Y
## 123.9545 154.7333SUMMARY STATISTICS We identified democratic nations and non-democratic nations from our sample countries within the prison population dataset for our analysis. For democratic nations our first and third quartile for prison population rates were 88.50 and 193.0 respectively. The median prison population rates in 2016 for democratic nations were 130.0. On average there were 154.7333 per 100,000 people in prison in 2016, with a standard deviation of 94.79487. On the other hand, non-democratic nations had a first quartile of 57.25 and a third quartile of 149.5. The median prison population rates in 2016 for non-democratic nations was 114.5. Our data showed on average non-democratic institutions had 123.9545 per 100,000 people in prison with a standard deviation of 99.00239.
#Summary Statistics for Prison Population Rates
sum_prison <- favstats( Rate.y ~ Democracy , data = prison_population)| Democracy | min | Q1 | median | Q3 | max | mean | sd | n | missing |
|---|---|---|---|---|---|---|---|---|---|
| N | 28 | 57.25 | 114.5 | 149.5 | 492 | 123.9545 | 99.00239 | 22 | 4 |
| Y | 58 | 88.50 | 130.0 | 193.0 | 411 | 154.7333 | 94.79487 | 15 | 0 |
Battle Deaths Due to Civil Conflict
For this type of violence we chose to only visualize battle deaths due to civil conflict for democratic and non-democratic nations. For democratic nations (Fig. 3a), Greece had the highest amount of battle deaths (38,500 deaths from 1946-1949) and the United Kingdom had the lowest amount of battle deaths (55 deaths in 1998). Among the non-democratic nations (Fig. 3b), China had the most amount of battle deaths (350,000 deaths from 1948-1949) and Malaysia had the least amount of battle deaths (13 deaths in 1960). Ethiopia and Iran have negative values, which means no battle deaths occurred.
The P-value is 0.7599 which means our data are not statistically significant and our test is inconclusive. Therefore, we have no evidence that there is a relationship between a nation’s battle deaths and whether that nation is democratic or non-democratic.
t.test(Death ~ Democracy , data = Battle_Death)##
## Welch Two Sample t-test
##
## data: Death by Democracy
## t = 0.30634, df = 113.54, p-value = 0.7599
## alternative hypothesis: true difference in means is not equal to 0
## 95 percent confidence interval:
## -5222.657 7133.276
## sample estimates:
## mean in group N mean in group Y
## 5753.370 4798.061SUMMARY STATISTICS We identified democratic nations and non-democratic nations from our sample countries within the battle deaths dataset for our analysis. For democratic nations the median battle deaths due to civil conflict were 111 in democratic nations. The mean battle deaths was 4798.061 with a standard deviation of 12713.63. On the other hand, the median battle deaths due to civil conflict for non-democratic nations was 27. The mean battle deaths was 5753.37 with a standard deviation of 36828.77.
#Summary Statistics for Battle Deaths in Democratic Nations
sum_Y_Battle <- favstats( ~ Death, data = Y_Dem_Battle_1)| min | Q1 | median | Q3 | max | mean | sd | n | missing | |
|---|---|---|---|---|---|---|---|---|---|
| -999 | 81 | 111 | 295 | 38500 | 4798.061 | 12713.63 | 33 | 0 |
#Summary Statistics for Battle Deaths in Non-Democratic Nations
sum_N_Battle <- favstats( ~ Death, data = N_Dem_Battle_1)| min | Q1 | median | Q3 | max | mean | sd | n | missing | |
|---|---|---|---|---|---|---|---|---|---|
| -999 | -999 | 27 | 1000 | 350000 | 5753.37 | 36828.77 | 281 | 0 |
Civil Rights Violation
Figure 4a and 4b illustrate civil rights violations for democratic and non-democratic nations in 2011. The type of violation was extrajudicial killings, which means governments who kill civilians without due process. The frequency index ranges from 0-2, where 0 means the killings occur frequently and 2 means the killings rarely occur or the killings were not recorded. Our data was statistically significant (P= 0.02865), which means that there is evidence of a relationship between civil rights violations and a nation’s form of government.
t.test(KILL ~ Democracy , data = civil_rights)##
## Welch Two Sample t-test
##
## data: KILL by Democracy
## t = -2.3005, df = 29.616, p-value = 0.02865
## alternative hypothesis: true difference in means is not equal to 0
## 95 percent confidence interval:
## -0.96757730 -0.05726742
## sample estimates:
## mean in group N mean in group Y
## 1.130435 1.642857SUMMARY STATISTICS We identified democratic nations and non-democratic nations from our sample countries within the civil rights dataset for our analysis. For democratic nations, the median frequency of extrajudicial killings in 2011 was 2, and the mean frequency of extrajudicial killings was 1.642857, with a standard deviation of 0.6333237. In non-democratic nations, the median frequency of extrajudicial killings in 2011 was 1, and the mean was 1.130435, with a standard deviation of 0.6944159. Our data shows that non-democratic governments commit more extrajudicial killings than democratic governments.
#Summary Statistics for Extrajudicial Killings
sum_civil <- favstats(KILL ~ Democracy , data = civil_rights)| Democracy | min | Q1 | median | Q3 | max | mean | sd | n | missing |
|---|---|---|---|---|---|---|---|---|---|
| N | 0 | 1.00 | 1 | 2 | 2 | 1.130435 | 0.6944159 | 23 | 3 |
| Y | 0 | 1.25 | 2 | 2 | 2 | 1.642857 | 0.6333237 | 14 | 1 |
Multiple Regression
| term | estimate | std_error | statistic | p_value | lower_ci | upper_ci |
|---|---|---|---|---|---|---|
| intercept | 6.10967 | 0.73751 | 8.28420 | 0.00000 | 4.65744 | 7.56189 |
| Prison | 0.00733 | 0.00244 | 3.00486 | 0.00292 | 0.00253 | 0.01213 |
| KILL | -0.87008 | 0.55377 | -1.57119 | 0.11735 | -1.96050 | 0.22035 |
| Death | -0.00002 | 0.00001 | -3.45440 | 0.00064 | -0.00003 | -0.00001 |
| DemocracyY | -4.97996 | 0.61230 | -8.13321 | 0.00000 | -6.18563 | -3.77428 |
\(\widehat{Homicide Rates} = 6.10967 + 0.00733 * Prison -0.87008 * KILL -0.00002 * Death -4.97996 * DemocracyY\)
For every one unit increase in Prison Population Rates, the predicted homicide rates increases by 0.00733.
For every one unit increase in extrajudicial killings, the predicted homicide rates decreases by -0.87008 (which makes sense because an extrajudicial killing of 2 means it happens infrequently.)
For every one unit increase in battle deaths, the predicted homicide rates decrease by -0.00002.
For every one unit increase in Democracy (where 0 is democracy and 1 is non-democracy), the predicted homicide rates decrease by -4.97996.
#actual coefficients
Total_Violence %>% select(Homicide, Prison, KILL, Death)%>%
cor(use="complete.obs") ## Homicide Prison KILL Death
## Homicide 1.00000000 0.12965994 -0.04897139 -0.16610818
## Prison 0.12965994 1.00000000 -0.11015492 -0.03329624
## KILL -0.04897139 -0.11015492 1.00000000 -0.29115125
## Death -0.16610818 -0.03329624 -0.29115125 1.00000000We do not have much correlation between the levels of violence. Battle deaths due to civil conflict and the frequency of judicial killings appear to have a small negative correlation (-0.29115125), but overall correlations between different levels of violence are insignificant.
CHECKING CONDITIONS In order to run a multiple regression, the residuals must be linear. They must also have consistant variance and must be normally distributed.
The residuals appear to be somewhat linear, though it is hard to tell whether there is equal variance. 
The residuals are not normally distributed, they are right-skewed.
Therefore, the conditions for multiple regression are not met. However, for the sake of this project we assumed the conditions were met.
ANOVA For Multiple Regression
In order to run an Analysis of Variance test, the residuals must be linear. They must also have consistant variance and must be normally distributed. As shown in the multiple regression section, the conditions are not met. However, for the sake of this project we will continue on assuming the conditions are met.
| Df | Sum Sq | Mean Sq | F value | Pr(>F) | |
|---|---|---|---|---|---|
| Prison | 1 | 61.922866 | 61.922866 | 5.7928261 | 0.0167868 |
| KILL | 1 | 4.486604 | 4.486604 | 0.4197176 | 0.5176475 |
| Death | 1 | 119.824986 | 119.824986 | 11.2095150 | 0.0009337 |
| Democracy | 1 | 707.105492 | 707.105492 | 66.1490556 | 0.0000000 |
| Residuals | 261 | 2789.979869 | 10.689578 | NA | NA |
According to the p-values present in the ANOVA table, Prison rates, Battle Deaths and Democracy are all good indicators that the model is effective at predicting homicide rates.
VI. Discussion
Given our alpha level of five percent, we do not reject the null hypotheses that homicide rates, prison populations, and battle deaths due to civil conflicts are not correlated. We do not have sufficient evidence to suggest that democratic institutions have lower levels of violence in these categories when compared to non-democratic institutions. However, with an alpha level of five percent, we can reject the null hypotheses that there is no relationship between civil rights violations, defined by extrajudicial killings, and whether or not a nation is a democracy. Our data presented significant evidence that democratic institutions have lower frequencies of extrajudicial killings. Essentially non-democratic governments killed their civilians without due process more frequently than democratic governments. Since three of the four levels of violence depicted no relationship between violence and whether or not a country was a democracy, we have evidence to contest the popular political theory that democracies are more peaceful.
Limitations and Possible Errors
Our project tested a generally accepted theory, which can have implaction on how future nations approach their government institutions. With this in mind, it is crucial that we discuss some of the limitations and possible errors throughout our analyses to avoid misunderstandings in our results and ensure future researchers can duplicate or improve upon our study.
First and foremost, our definition and measurement criteria of democracy is not universal. Before we ran these statistical analyses, we recognized that in today’s political climate the terms democratic and non-democratic are incredibly vague. There are dozens of variations of democratic institutions and hundreds of non-democratic forms of government, which in some ways are vastly interconnected. Our strict criteria, using only three indicators of democracy with a high cutoff, was an attempt to differentiate general democracies and non-democracies while not excluding either form’s different variations. In some cases this distinction was successful but in others some countries were considered non-democratic when in reality they are considered democratic and vice-versa. As a result, our sample is not representative of the actual global institutions present, so rejecting the political theory only applies to those who agree with our definition of democracy.
It is important to reiterate that there were some inconsistencies and unknown values in our datasets. Our method of finding countries was heavily reliant on how a country was named. Throughout different datasets, countries were named differently due to abbreviations, different spellings, and the change in a country’s name over time. If there were mismatched names, the country would be not be collected in our filter method and would be considered an unknown value, which impacted our results. For example, the United States was considered unknown in some datasets since it would be referred to as US, USA, or the United States of America, rather than the United States. Furthermore, among all four data sets, data collection for each country was inconsistent. This made it difficult to assess levels of violence at one point in time as some countries would have higher levels of violence due to having more data for that year rather than being more violent. Finally, all of this data is observational, so we can never claim causality.
Further Research
Throughout our observations, we did notice some trends that inspired some interesting implications for each level of violence. For instance, in non-democratic nations there were higher homicide rates and battle deaths due to civil conflict, while in democratic nations prison population rates were higher. If the data were statistically significant, the visualizations could have suggested that democratic nations were less violent because more criminals are in jail. Although one cannot rely on visualizations to make causal conclusions or strong correlations, these observations do bring about ideas for future research. We would be interested in exploring whether rates of violence differ significantly among different types of non-democratic institutions and whether those rates change among nations who transition from non-democratic to democratic governments and vice versa. Overall, we would like to examine how a country evolves politically and whether that evolution reveals new factors that result in the trends present in our report.
VII. Conclusion
Our data analyses do not support the political theory that democratic institutions reduce the levels of violence worldwide. Although there may appear to be some trends that identify correlations between levels of violence and forms of government, these trends are statistically insignificant and are likely a result of other confounding variables. Therefore, we cannot support the claim that democratic nations are more peaceful.
VIII. Citations
“Global Standards, Local Knowledge.” V, www.vdem.net/en/analysis/MapGraph/.
“Intentional Homicide Victims | Statistics and Data.” United Nations, United Nations, dataunodc.un.org/crime/intentional-homicide-victims.
“Intentional Homicide Victims | Statistics and Data.” United Nations, United Nations, dataunodc.un.org/crime/intentional-homicide-victims.
Peace Pesearch Institute Oslo. “The Battle Deaths Dataset Version 3.0.” PRIO, www.prio.org/Data/Armed-Conflict/Battle-Deaths/The-Battle-Deaths-Dataset-version-30/.
Unknown. “CIRI Human Rights Data Project.” CIRI Human Rights Data Project, 1 Jan. 1970, www.humanrightsdata.com/.
Appendix: Statistical Analyses
In order to make it easier for the reader to grade our assignment, we have compiled all of our statistical analyses here. The material in this appendix is contained in the document above, however, in this section the material is organized according to the rubric.
1. Summary Statistics for Each Variable
Homicide Rates in 2016
#Summary Statistics for Homicide Rates
sum_hom <- favstats( Rate ~ Democracy, data = foo)| Democracy | min | Q1 | median | Q3 | max | mean | sd | n | missing |
|---|---|---|---|---|---|---|---|---|---|
| N | 0.9165611 | 2.052631 | 3.104113 | 4.375431 | 13.48376 | 3.969053 | 3.057837 | 26 | 0 |
| Y | 0.6388674 | 0.909254 | 1.268179 | 2.271686 | 15.74518 | 2.579143 | 3.828091 | 15 | 0 |
t.test(Rate ~ Democracy , data = foo)##
## Welch Two Sample t-test
##
## data: Rate by Democracy
## t = 1.2022, df = 24.356, p-value = 0.2408
## alternative hypothesis: true difference in means is not equal to 0
## 95 percent confidence interval:
## -0.9943315 3.7741507
## sample estimates:
## mean in group N mean in group Y
## 3.969053 2.579143Prison Population Rates in 2016
#Summary Statistics for Prison Population Rates
sum_prison<- favstats( Rate.y ~ Democracy , data = prison_population)## Warning in (function (x, ..., na.rm = TRUE, type = 7) : Auto-converting
## character to numeric.
## Warning in (function (x, ..., na.rm = TRUE, type = 7) : Auto-converting
## character to numeric.| Democracy | min | Q1 | median | Q3 | max | mean | sd | n | missing |
|---|---|---|---|---|---|---|---|---|---|
| N | 28 | 57.25 | 114.5 | 149.5 | 492 | 123.9545 | 99.00239 | 22 | 4 |
| Y | 58 | 88.50 | 130.0 | 193.0 | 411 | 154.7333 | 94.79487 | 15 | 0 |
Battle Deaths due to Civil Conflict (1946 - 2008)
#Summary Statistics for Battle Deaths in Democratic Nations
sum_D_Battle <- favstats( ~ Death, data = Y_Dem_Battle_1)| min | Q1 | median | Q3 | max | mean | sd | n | missing | |
|---|---|---|---|---|---|---|---|---|---|
| -999 | 81 | 111 | 295 | 38500 | 4798.061 | 12713.63 | 33 | 0 |
#Summary Statistics for Battle Deaths in Non-Democratic Nations
sum_N_Battle <- favstats( ~ Death, data = N_Dem_Battle_1)| min | Q1 | median | Q3 | max | mean | sd | n | missing | |
|---|---|---|---|---|---|---|---|---|---|
| -999 | -999 | 27 | 1000 | 350000 | 5753.37 | 36828.77 | 281 | 0 |
Civil Rights Violation: Extrajudicial Killings in 2011
#Summary Statistics for Extrajudicial Killings
sum_civil <- favstats(KILL ~ Democracy , data = civil_rights) | Democracy | min | Q1 | median | Q3 | max | mean | sd | n | missing |
|---|---|---|---|---|---|---|---|---|---|
| N | 0 | 1.00 | 1 | 2 | 2 | 1.130435 | 0.6944159 | 23 | 3 |
| Y | 0 | 1.25 | 2 | 2 | 2 | 1.642857 | 0.6333237 | 14 | 1 |
2. Descriptive and Comparative Graphics
Barplot for Homicide Rates in 2016
The barplot depicts the Bahamas, whose type of government is unknown, as having the highest homicide rate and the United Kingdom, a democratic country, as having the lowest homicide rate (Fig. 1a). Among democratic nations, the highest homicides rates were located in Panama—a total of 1,574,518 people per year—while the lowest homicide rates were found in the United Kingdom—total of 63,886.74 people per year. For non-democratic nations the highest homicide rates were located in the Dominican Republic, with an estimate of 1,348,376 people per year, while the lowest homicide rates were present in Burkina Faso, with an estimate of 91,656.11 people per year.
Barplot for Prison Population Rates in 2016
Although there appears to be a trend between a nation’s prison rates and whether that nation is democratic or non-democratic, the relationship between these two variables is not statistically significant. With a p-value of 0.3483, we find no evidence that prison populations are correlated to the type of government institution. Overall, the United States has the highest prison population rates (718 per 100,000 people), and Burkina Faso has the lowest prison population rates (28 per 100,000 people).
Barplot for Battle Death Rates Due to Civil Conflict (1946 - 2008)
For this type of violence we chose to only visualize battle deaths due to civil conflict for democratic and non-democratic nations. For democratic nations (Fig. 3a), Greece had the highest amount of battle deaths (38,500 deaths from 1946-1949) and the United Kingdom had the lowest amount of battle deaths (55 deaths in 1998). Among the non-democratic nations (Fig. 3b), China had the most amount of battle deaths (350,000 deaths from 1948-1949) and Malaysia had the least amount of battle deaths (13 deaths in 1960). Ethiopia and Iran have negative values which means there were no battle deaths occurred or were recorded.
Civil Rights Violation: Extrajudicial Killings in 2011
Figure 4a and 4b illustrate civil rights violations for democratic and non-democratic nations in 2011. The type of violation was extrajudicial killings, which means governments who kill civilians without due process. The frequency index ranges from 0-2, where 0 means the killings occur frequently and 2 means the killings rarely occur or the killings were not recorded. Our data was statistically significant (P= 0.02865), which means that there is evidence of a relationship between civil rights violations and a nation’s form of government.
3. Descriptive Analysis of Relationship Between
Homicide Rates 2016
4. Anything Unusual in the Data
A. Democracy Index The index was determined by five expert social science research methodologists. However, the indices are somewhat subjective as they were determined by research methodologists. One could argue that there is always some level of bias present when a decision is made by a human. This could result in potential biases for our definition of a democracy. We also used a high index requirement of 0.75. If we accepted nations with indexes greater than or equal to 0.5, our data may have been different as nations previously coded as non-democratic would now be considered democratic. Therefore, there are some potential biases in our coding of democratic and non-democratic nations.
B. Homicide Rates For the statistical analyses, we calculated a difference in means between democratic and non-democratic nations, so the cases were 16 democratic nations (there was missing data for the United States) and 26 non-democratic nations.
C. Prison Population Rates The cases for the statistical analyses were 15 of the 16 democratic nations (data were missing for the US) and 22 of the 26 non-democratic nations (data were missing for Bolivia, Burkina Faso, Iran, and Moldova).
D. Battle Deaths There were gaps in the data which meant we could not filter for one specific year. Therefore, we only filtered for the type of democracy. This meant that for the democratic nations, we had 33 cases and for non-democratic nations, we had 281 cases.
E. Extrajudicial Killings The cases for the data visualization and statistical analyses were 14 of the 16 democratic nations (data were missing for Slovakia and the US) and 23 of the 26 non-democratic nations (data were missing for Congo, Kyrgyzstan, and Timor.)
Other It is also important to note that if a name of a country did not exactly match the name contained in the data set, it was automatically considered an unknown democracy. This explains why the US was unknow. Our democracy data set that we created listed the US as United States America, whereas other data sets listed it as US or United States.
5. Confidence Interval, Difference in Mean, Multiple Regression
A. Confidence Interval
In order to conduct a confidence interval the data must be bell-shaped and symmetrical.
The data are not bell-shaped or symmetrical—they are right skewed—so the conditions to run a 95% confidence interval are not met. However, for the sake of this report, we will continue on assuming that the conditions are met.
## Single numerical variable
## n = 26, y-bar = 3.9691, s = 3.0578
## 95% CI: (2.734 , 5.2041)
The 95% confidence interval for the mean rates of homicide rates in non-democratic nations is (2.734 , 5.2041). Therefore, we are 95% confident that the mean homicide rates in non-democratic nations is between 2.734 and 5.2041 per 100,000 people.
B. Difference In Means
The amount of cases (n) must be greater than or equal to 30, or the data must be symmetric. Our conditions are not met for a difference in means because we have 16 democratic nations and 26 non-democratic nations and the data is right-skewed. However, for the sake of this report, we will continue on assuming that the conditions are met.
t.test(Rate ~ Democracy , data = foo)##
## Welch Two Sample t-test
##
## data: Rate by Democracy
## t = 1.2022, df = 24.356, p-value = 0.2408
## alternative hypothesis: true difference in means is not equal to 0
## 95 percent confidence interval:
## -0.9943315 3.7741507
## sample estimates:
## mean in group N mean in group Y
## 3.969053 2.579143The difference in mean homicide rates for non-democratic and democratic nations is not statistically significant. With a p-value of 0.2408, we fail to reject the null hypothesis that the mean rates of homicide in democratic and non-democratic nations are equal. This test is inconclusive.
C. Multiple Regression
In order to run a multiple regression, the residuals must be linear. They must also have consistant variance and must be normally distributed.
The residuals appear to be somewhat linear, though it is hard to tell whether there is equal variance.
The residuals are not normally distributed, they are right-skewed.
Therefore, the conditions for multiple regression are not met. However, for the sake of this project we will continue on assuming the conditions are met.
#assessing colinearity
Total_Violence %>% select(Homicide, Prison, KILL, Death)%>%
pairs() 
#actual coefficients
Total_Violence %>% select(Homicide, Prison, KILL, Death)%>%
cor(use="complete.obs") ## Homicide Prison KILL Death
## Homicide 1.00000000 0.12965994 -0.04897139 -0.16610818
## Prison 0.12965994 1.00000000 -0.11015492 -0.03329624
## KILL -0.04897139 -0.11015492 1.00000000 -0.29115125
## Death -0.16610818 -0.03329624 -0.29115125 1.00000000| term | estimate | std_error | statistic | p_value | lower_ci | upper_ci |
|---|---|---|---|---|---|---|
| intercept | 6.10967 | 0.73751 | 8.28420 | 0.00000 | 4.65744 | 7.56189 |
| Prison | 0.00733 | 0.00244 | 3.00486 | 0.00292 | 0.00253 | 0.01213 |
| KILL | -0.87008 | 0.55377 | -1.57119 | 0.11735 | -1.96050 | 0.22035 |
| Death | -0.00002 | 0.00001 | -3.45440 | 0.00064 | -0.00003 | -0.00001 |
| DemocracyY | -4.97996 | 0.61230 | -8.13321 | 0.00000 | -6.18563 | -3.77428 |
\(\widehat{Homicide Rates} = 6.10967 + 0.00733 * Prison -0.87008 * KILL -0.00002 * Death -4.97996 * DemocracyY\)
For every one unit increase in Prison Population Rates, the predicted homicide rates increases by 0.00733.
For every one unit increase in extrajudicial killings, the predicted homicide rates decreases by -0.87008 (which makes sense because an extrajudicial killing of 2 means it happens infrequently.)
For every one unit increase in battle deaths, the predicted homicide rates decrease by -0.00002.
For every one unit increase in Democracy (where 0 is democracy and 1 is non-democracy), the predicted homicide rates decrease by -4.97996.
6. ANOVA
In order to run an Analysis of Variance test, the residuals must be linear. They must also have consistant variance and must be normally distributed. As shown in the multiple regression section, the conditions are not met. However, for the sake of this project we will continue on assuming the conditions are met.
| Df | Sum Sq | Mean Sq | F value | Pr(>F) | |
|---|---|---|---|---|---|
| Prison | 1 | 61.922866 | 61.922866 | 5.7928261 | 0.0167868 |
| KILL | 1 | 4.486604 | 4.486604 | 0.4197176 | 0.5176475 |
| Death | 1 | 119.824986 | 119.824986 | 11.2095150 | 0.0009337 |
| Democracy | 1 | 707.105492 | 707.105492 | 66.1490556 | 0.0000000 |
| Residuals | 261 | 2789.979869 | 10.689578 | NA | NA |
According to the p-values present in the ANOVA table, Prison rates, Battle Deaths and Democracy are all good indicators that the model is effective at predicting homicide rates.
7. Issues with our Data (Were conditions met for each test)
A. 95% Confidence Interval
The data must be bell-shaped and symmetrical.
The data are not bell-shaped or symmetrical, they are right skewed, so the conditions to run a 95% confidence interval are not met. However, for the sake of this report, we will continue on assuming that the conditions are met.
B. Difference in Means
The amount of cases (n) must be greater than or equal to 30, or the data must be symmetric. Our conditions are not met for a difference in means because we have 16 democratic nations and 26 non-democratic nations and the data is right-skewed. However, for the sake of this report, we will continue on assuming that the conditions are met.
C. Mulptiple Regression and ANOVA
The residuals must be linear. They must also have consistant variance and must be normally distributed.
The residuals appear to be somewhat linear, though it is hard to tell whether there is equal variance.
The residuals are not normally distributed, they are right-skewed. Therefore, the conditions for multiple regression and ANOVA are not met.